MATH 1B Lecture 23: Midterm II Review
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Math 1b: calculus - lecture 23: midterm ii review. Review midterm i material, may be included (1/y. 1/y = t: (dy/dt) = t2, dt = t2 dt. Q: solve dy/dt = t2y2 given that y=1 when t-0; t>=0. But y=1 when t=0, so -1/1 = 0 +c. This is valid for 0<=t<=3 3. c = -1. 3/3 + c. dx/dt = x(1-t)+1-t. dx/dt +(t-1)x = 1-t. So the integrating factor is p(x) = (t-1) dt = (t2/2) + t, so e p(x) = e((t^2)/2) +t . Let s denote the mass of salt in the tank in kg. Water flows into the tank at 10 l/min. Salt flows into the tank at . 1 kg salt/l. Water flows out of the tank at 10 l/min. The rate at which salt flows into the tank is (10 l/min)(. 1 kg salt/l) = 1 kg/l. The amount of salt in the tank at any given time is s.
